Hostname: page-component-5db58dd55d-h5th4 Total loading time: 0 Render date: 2026-05-25T23:28:52.940Z Has data issue: false hasContentIssue false
  • English
  • Français

Automatic methods for generating seismic intensity maps

Part of: Geophysics Geophysics (general) Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

David R. Brillinger ,
Chang Chiann ,
Rafael A. Irizarry  and
Pedro A. Morettin
David R. Brillinger*
Affiliation:
University of California, Berkeley
Chang Chiann*
Affiliation:
University of Sao Paulo
Rafael A. Irizarry*
Affiliation:
Johns Hopkins University
Pedro A. Morettin*
Affiliation:
University of Sao Paulo
*
1 Postal address: Department of Statistics, University of California, Berkeley, CA 94720, USA. Email: brill@stat.berkeley.edu
2 Postal address: Department of Statistics, University of São Paulo, SP 05315–970, Brazil.
3 Postal address: Department of Biostatistics, Johns Hopkins University, Baltimore, MD 21205, USA.
2 Postal address: Department of Statistics, University of São Paulo, SP 05315–970, Brazil.
Get access Rights & Permissions [Opens in a new window]

Abstract

For many years the modified Mercalli (MM) scale has been used to describe earthquake damage and effects observed at scattered locations. In the next stage of an analysis involving MM data, isoseismal lines based on the observations have been added to maps by hand, i.e. subjectively. However a few objective methods have been proposed (by e.g. De Rubeis et al., Brillinger, Wald et al. and Pettenati et al.). The work presented here develops objective methods further. In particular the ordinal character of the MM scale is specifically taken into account. Numerical smoothing is basic to the approach and methods involving splines, local polynomial regression and wavelets are illustrated. The approach also allows the inclusion of explanatory variables, for example site effects. The procedure is implemented for data from the 17 October 1989 Loma Prieta earthquake.

Keywords

Isoseismalslocal polynomialsMercalli scaleordinal datasmoothingsplineswavelets

MSC classification

Primary: 62M30: Spatial processes
Secondary: 86A15: Seismology

Information

Type
Models and statistics in seismology
Information
Journal of Applied Probability , Volume 38 , Issue A: Probability, Statistics and Seismology , 2001 , pp. 188 - 201
Copyright
Copyright © Applied Probability Trust 2001 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1] Bolt, B. A. (1993). Earthquakes. Freeman, New York.Google Scholar
[2] Brillinger, D. R. (1993). Earthquake risk and insurance. Environmetrics 4, 1–21.CrossRefGoogle Scholar
[3] Brillinger, D. R. (1994). Trend analysis: time series and point process problems. Environmetrics 5, 11–19.Google Scholar
[4] Brillinger, D. R. (1994). Examples of scientific problems and data analyses in demography, neurophysiology and seismology. J. Comp. Graph. Statist. 3, 1–22.Google Scholar
[5] Brillinger, D. R. (1996). An analysis of an ordinal-valued time-series. In Proc. Athens Conf. Appl. Probab. and Time Series (Lecture Notes Statist. 115), Springer, Berlin, 74–87.Google Scholar
[6] Brillinger, D. R. (1997). Random process methods and environmental data: the 1996 Hunter lecture. Environmetrics 8, 269–281.Google Scholar
[7] Brillinger, D. R. (2000). Some examples of random process environmental data analysis. In Bioenvironmental and Public Health Statistics (Handbook Statist. 18), eds Sen, P. K. and Rao, C. R., Elsevier, Amsterdam, 33–56.Google Scholar
[8] Brillinger, D. R., Morettin, P. A., Irizarry, R. A. and Chiann, C. (2000). Some waveletbased analyses of Markov chain data. Signal Processing 80, 1607–1627.Google Scholar
[9] Bruce, A. and Gao, H.-Ye (1996). Applied Wavelet Analysis with S-PLUS. Springer, New York.Google Scholar
[10] Bullen, K. E. and Bolt, B. A. (1985). An Introduction to the Theory of Seismology , 4th edn. Cambridge University Press.Google Scholar
[11] Chiann, C. and Morettin, P. A. (1999). Estimation of time-varying linear systems. Statist. Inf. Stoch. Proc. 2, 253–285.Google Scholar
[12] Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. J. Amer. Statist. Assoc. 74, 829–836.Google Scholar
[13] Cleveland, W. S., Grosse, E. and Shyu, W. M. (1992). Local regression models. In Statistical Models in S , eds Chambers, J. M. and Hastie, T. J., Wadsworth, Pacific Grove, CA, 309–376.Google Scholar
[14] Daubechies, I. (1992). Ten Lectures on Wavelets. SIAM, Philadelphia.Google Scholar
[15] De Rubeis, V., Gasparini, C., Maramai, A., Murru, M. and Tertulliani, A. (1992). The uncertainty and ambiguity of isoseismal maps. Earthquake Eng. Structural Dynamics 21, 509–523.CrossRefGoogle Scholar
[16] Donoho, D. L. and Johnstone, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81, 425–455.CrossRefGoogle Scholar
[17] Efron, B. and Tibshirani, R. (1993). An Introduction to the Bootstrap. Chapman and Hall, London.CrossRefGoogle Scholar
[18] Fahrmeir, L. and Tutz, G. (1994). Multivariate Statistical Modelling Based on Generalized Linear Models. Springer, New York.Google Scholar
[19] Hastie, T. J. (1992). Generalized additive models. In Statistical Models in S , eds Chambers, J. M. and Hastie, T. J., Wadsworth, Pacific Grove, CA, 249–308.Google Scholar
[20] Hastie, T. J. and Tibshirani, R. (1990). Generalized Additive Models. Chapman and Hall, London.Google Scholar
[21] Justo, J. L. and Salwa, C. (1998). The 1531 Lisbon earthquake. Bull. Seismol. Soc. America 88, 319–328.Google Scholar
[22] Mccullagh, P. (1980). Regression models for ordinal data (with discussion). J. Roy. Statist. Soc. Ser. B 42, 109–142.Google Scholar
[23] Mccullagh, P. and Nelder, J. A. (1989). Generalized Linear Models , 2nd edn. Chapman and Hall, New York.CrossRefGoogle Scholar
[24] Musmeci, F. (1984). A method for drawing confidence bounds on seismic contour maps. Italian National Agency for Nuclear and Alternative Energy Sources (ENEA), Rome.Google Scholar
[25] Perkins, J. B. and Boatwright, J. (1995). On Shaky Ground. ABAG, Oakland, CA.Google Scholar
[26] Pettenati, F., Sirovich, L. and Cavallini, F. (1999). Objective treatment and synthesis of macroseismic intensity data sets using tesselation. Bull. Seismol. Soc. America 89, 1203–1213.Google Scholar
[27] Pregibon, D. (1980). Discussion of ‘Regression models for ordinal data’ by P. McCullagh. J. Roy. Statist. Soc. Ser. B 42, 138–139.Google Scholar
[28] Reiter, L. (1990). Earthquake Hazard Analysis. Columbia University Press, New York.Google Scholar
[29] Silverman, B. W. (1985). Some aspects of the spline smoothing approach to non-parametric regression curve fitting. J. Roy. Statist. Soc. Ser. B 47, 1–21.Google Scholar
[30] Stover, C. W., Reagor, B. G., Baldwin, F. and Brewer, L. R. (1990). Preliminary isoseismal map for the Santa Cruz (Loma Prieta), California, earthquake of October 18, 1989 UTC. Open-File Report 90-18, National Earthquake Information Center, Denver.Google Scholar
[31] Vere-Jones, D. (1970). Stochastic models for earthquake occurrence (with discussion). J. Roy. Statist. Soc. Ser. B 32, 1–62.Google Scholar
[32] Vere-Jones, D. and Smith, E. G. C. (1981). Statistics in seismology. Commun. Statist.-Theor. Meth. A10, 1559–1585.CrossRefGoogle Scholar
[33] Vidakovic, B. (1999). Statistical Modeling by Wavelets. Wiley, New York.Google Scholar
[34] Wahba, G. (1990). Spline Models for Observational Data (CBMS-NSF Regional Conference Series). SIAM, Philadelphia.Google Scholar
[35] Wald, D. J., Quitoriano, V., Dengler, L. A. and Dewey, J. W. (1999). Utilization of the internet for rapid community intensity maps. Seismol. Res. Lett. 70, 680–697.CrossRefGoogle Scholar